Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.29792 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- The $(-1)$-Jacobi, Bannai-Ito, and $(-1)$-Meixner-Pollaczek polynomials are studied in [Trans. Amer. Math. Soc. 364 (2012), 5491-5507], [Adv. Math. 229 (2012), 2123-2158], and [Stud. Appl. Math. 153 (2024), e12728], respectively, through polynomial eigenfunctions of first-order Dunkl operators. The purpose of the present note is to show that these families are not isolated phenomena, but particular instances of a single alternating mechanism which is most naturally formulated at the level of orthogonality functionals, transpose operators, and structural identities. This functional-analytic point of view also leads to an explicit algorithm which, starting from an ordinary orthogonal polynomial sequence in the quadratic variable, systematises the construction of such $(-1)$-classical families.